Supplementary Information: Supplementary Figure 1. Resistance dependence on pressure in the semiconducting region.

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1 Supplementary Information: Supplementary Figure 1. Resistance dependence on pressure in the semiconducting region. The pressure activated carrier transport model shows good agreement with the experimental data. 1

2 Supplementary Figure 2. Theoretical temperature-dependent resistivity of MoS 2 at selected pressures. (a) Semiconducting state, and (b) metallic state. 2

3 Supplementary Figure 3. Angular momentum projected density of states (LDOS) of Mo and S in multilayered MoS 2 at representative pressures. (a) and (b) are LDOS at 0 and 29.6 GPa, respectively. Zoom in of the LDOS at (c) 0 GPa, and (d) 29.6 GPa. The Fermi level is at 0 ev. 3

4 Supplementary Figure 4. Raman intensity ratio. I A1g /I E2g ratio as a function of pressure shows an increase in the IS region. The maximum intensity ratio is observed in the metallic state. The insets shows the relative intensities of the E 2g and A 1g peaks at selected pressures. Supplementary Figure 5. Theoretically predicted phonon bands at representative pressures. The results indicate that the splitting in the bands increases with increasing pressure. The E 2g (blue line) and A 1g (red line) modes are identified from the dispersion curves at the Γ point and their frequencies at ambient conditions are cm -1 and cm -1, respectively. 4

5 Supplementary Figure 6. Theoretically-predicted XRD results for multilayered MoS 2 as a function of pressure. The d-spacings of representative lattice planes as a function of pressure. No new peaks are observed. 5

6 Supplementary Figure 7. Electron microprobe analyses of the multilayered MoS 2 sample. (a) HR-TEM image of the honeycomb structural arrangement of the multilayered MoS 2. Inset: FFT image of the pristine multilayered MoS 2 sample. (b) Cross-sectional HR-TEM image of a multilayered MoS 2 before compression showing the interlayer distance to be approximately 6.5 Å. (c) TEM-EDX spectra of the multilayered crystalline MoS 2 after decompression. (d) SEM-EDX spectra for the multilayered MoS 2. Inset: SEM images are shown before loading and after decompression. 6

7 Supplementary Figure 8. Pressure-strain relation and the theoretical band gap dependence on strain. (a) Pressure relationship to compressive strain, which allows correlation of the theoretical pressures in this work to strain. The red line is a quadratic fit to the data. (b) Band gap reduction with normal compressive strain applied to multilayered (bi-layer, tri-layer, four-layer, five-layer, six-layer and bulk) MoS 2. (c) Predicted critical strain threshold ( th ) as a function of the number of layers. The critical strain threshold is the strain corresponding to the closure of the band gap. 7

8 Supplementary Note 1 The pressure dependent resistivity in the semiconducting state (SC) can be understood within the context of pressure activated conduction of dopant or defect states, consistent with prior reports of the reduction of dopant activation energy (E A ) with increasing pressure in MoS 2 crystals [1]. We note that n-type carrier conduction is the dominant transport mechanism in mined natural MoS 2 materials [1,2,3]. In a careful study by Hinkle and co-workers on MoS 2 obtained from the same supplier (SPI), native defects such as interstitials and vacancies were found to be responsible for the defect or dopant states rather than external impurity atoms. This is consistent with our elemental analysis (Figure S7), and overall the material can be summarized to be of high chemical purity but with native defects. On this basis, the effects of external chemical dopants and intercalated chemical species can be ruled out. The pressure activated model assumes a weak or negligible mobility dependence on pressure, justified by a prior experimental study of n-type MoS 2 [1]. To first order, the activation energy can be described by E A =E AO -mp in the semiconducting state [4,5]. E AO, m, and P are the activation energy at ambient pressure, linear coefficient of the pressure dependent activation energy, and applied pressure respectively. Analytically, the resistivity can be captured by an exponential model as is appropriate in the semiconducting state, ρ=ρ o exp((e A -E AO )/E th )=ρ o exp(-mp/e th ), where ρ o is the ambient resistivity and E th is the thermal energy. The pressure activated model proves adequate in understanding the resistivity or resistance dependence on pressure in the semiconducting state and shows good agreement to the experimental data (Figure S1). The best fit value of the linear coefficient is m 9.7 mev/gpa within the range of values (~7-26 mev/gpa) of a previous study on MoS 2 [1], and within a factor of two of a recent study on WSe 2 [4]. 8

9 Supplementary References [1] A. J. Grant et al.the electrical properties and the magnitude of the indirect gap in the semiconducting transition metal dichalcogenide layer crystals, Journal of Physics C: Solid State Physics, 8, L17, [2] B. W. H. Baugher et al., Intrinsic Electronic Transport Properties of High-Quality Monolayer and Bilayer MoS 2, Nano Letters, 13, , [3] S. McDonnell et al. "Defect-Dominated Doping and Contact Resistance in MoS2," ACS Nano (ASAP), [4] B. Liuet al.pressure Induced Semiconductor-Semimetal Transition in WSe 2, The Journal of Physical Chemistry C, 114, , [5] A. Jayaraman et al. Pressure-Induced Metal-Semiconductor Transition and 4f Electron Delocalization in SmTe, Physical Review Letters, ,